Another set of infinitely many exceptional (X) Laguerre polynomials
Abstract
We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one dimensional quantum mechanics and the corresponding X Laguerre and Jacobi polynomials (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417). The new X Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known X Jacobi polynomials and the potentials, whereas the known X Laguerre polynomials and the potentials are obtained in the same manner from the mirror image of the known X Jacobi polynomials and the potentials.
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